Regarding the Navier slip coefficient, in its dimensional form it is given by \(\varsigma =\mu /l_s\) , where \(l_s\)  is the slip length (see [1]}, [2]}, [3]}, [4]}). \(l_s\)  is typically of order \(10^{-9}\)  m (i.e. order of nanometers) but it can be greatly altered on manufactured surfaces by, e.g, applying hydrophobic coatings ([5]}). For example, in [4]}, surfaces with slip length greater than 25 \(\mu \) m have been reported. Using the physical quantities typical for water, the slip coefficient in its dimensionless form (used in this paper) can be estimated to be of order \(10^{-1}\sim 10^4\)  (from surfaces with large to small slip length). For the purposes of this paper, hydrophobic surfaces with large slip length are of the main interest, on which droplets are able to depin and start moving.
